The line $l$ passes through the points $A$ and $B$ with coordinates $(1,2,4)$ and \((-2,3,1)

Question

The line $l$ passes through the points $A$ and $B$ with coordinates $(1,2,4)$ and $(-2,3,1)$ respectively. The plane $p$ has equation $3x-y+2z=17$. Find the coordinates of the point of intersection of $l$ and $p$,[5] the acute angle between $l$ and $p$,[3] the perpendicular distance from $A$ to $p$ .[3]

Accepted Answer

(i) $\left(\frac52,\frac32,\frac{11}2\right)$ (ii) $78.8^\circ$ (iii) $\frac8{\sqrt{14}}$ units

N2007 P1 Q8

N2007 P1 Q8

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